In this course we will extend our theory of calculus to cover functions of multiple variables. We will understand these functions algebraically and geometrically, and learn how to use the tools of differential and integral calculus to further understand them.
Topics will include: 3D graphing, planes, partial derivatives, vectors, directional derivatives, gradients, the chain rule, optimization and Lagrange multipliers, integration, parametrization, vector fields, line and surface integrals, and Green’s, Stokes’s, and the Divergence theorem.
The course syllabus is available here.
- Complete Notes
- Section 1: Multivariable Functions
- Section 2: Vectors
- Section 3: Derivatives
- Section 4: Optimization
- Section 5: Integrals
- Section 6: Parametrization
- Section 7: Line Integrals
- Section 8: Surface Integrals
- Section 9: Divergence and Differential Forms
- Homework 1, due on Wednesday, January 31.
- Homework 2, due on Wednesday, February 7.
- Homework 3, due on Wednesday February 14
- Practice homework 3.5 for test on Wednesday February 21
- Homework 4, due on Wednesday February 28
- Homework 5, due on Wednesday March 7
- Practice homework 5.5 for test on Wednesday March 21
- Homework 6, due on Wednesday March 28
- Homework 7, due on Wednesday April 4
- Practice homework 7.5 for test on Wednesday April 11
- Homework 8, due on Wednesday April 18
- Homework 9, due on Wednesday April 25
- Final Practice Homework for final on Friday May 12
Tentative midterm dates are February 21, March 21, and April 11.
The final exam is at 1:00 PM on Friday, May 11, in the usual classroom.
Graphing calculators will not be allowed on tests.
Scientific, non-programmable calculators will be allowed. I will
have some to share, but not enough for everyone.
You can download Mathematica by following this link. You will be asked to create an account. After you have created an account and logged in, return to that link to download Mathematica for your computer.
The official textbook for this course is Calculus: Multivariable, 6th edition, by William McCallum et al. The ISBN is 978-0470888674.